Almost Increasing Sequence

Given a sequence of integers as an array, determine whether it is possible to obtain a strictly increasing sequence by removing no more than one element from the array.

Note: sequence a0, a1, ..., an is considered to be a strictly increasing if a0 < a1 < ... < an. Sequence containing only one element is also considered to be strictly increasing.

Example

almost_increasing_sequence(sequence) = false

There is no one element in this array that can be removed in order to get a strictly increasing sequence.

• For sequence = [1, 3, 2], the output should be

  almost_increasing_sequence(sequence) = true

  You can remove 3 from the array to get the strictly increasing sequence [1, 2]. Alternately, you can remove 2 to get the strictly increasing sequence [1, 3].

Solution

PYTHON

def almost_increasing_sequence(sequence):
    droppped = False
    last = prev = min(sequence) - 1
    for elm in sequence:
        if elm <= last:
            if droppped:
                return False
            else:
                droppped = True
            if elm <= prev:
                prev = last
            elif elm >= prev:
                prev = last = elm
        else:
            prev, last = last, elm
    return True

JAVASCRIPT

function almostIncreasingSequence(sequence) {
  let count = 0;
  for (let i = 0; i < sequence.length; i++) {
    if (sequence[i] <= sequence[i - 1]) {
      count++;
      if (sequence[i] <= sequence[i - 2] && sequence[i + 1] <= sequence[i - 1]) {
        return false;
      }
    }
  }
  return count <= 1;
}

console.log(almostIncreasingSequence([1, 3, 2]));